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@article{949843,
author = {Šimon Hilscher, Roman and Zemánek, Petr},
article_location = {Delhi},
article_number = {1},
keywords = {Time scale; Weyl-Titchmarsh theory; Second order Sturm-Liouville dynamic equation; m(λ)-function; Weyl disk; Weyl circle; Limit point case; Limit circle case},
language = {eng},
issn = {0973-6069},
journal = {Int. J. Difference Equ.},
title = {Overview of Weyl-Titchmarsh theory for second order Sturm-Liouville equations on time scales},
volume = {6},
year = {2011}
}
TY - JOUR
ID - 949843
AU - Šimon Hilscher, Roman - Zemánek, Petr
PY - 2011
TI - Overview of Weyl-Titchmarsh theory for second order Sturm-Liouville equations on time scales
JF - Int. J. Difference Equ.
VL - 6
IS - 1
SP - 39-51
EP - 39-51
PB - Research India Publications
SN - 09736069
KW - Time scale
KW - Weyl-Titchmarsh theory
KW - Second order Sturm-Liouville dynamic equation
KW - m(λ)-function
KW - Weyl disk
KW - Weyl circle
KW - Limit point case
KW - Limit circle case
N2 - In this paper we present an overview of the basic Weyl-Titchmarsh theory for second order Sturm-Liouville equations on time scales. We construct m(lambda)-function, the Weyl solution, and Weyl disk. We justify the terminology ``disk'' by its geometric properties, show explicitly the coordinates of the center of the disk, and calculate its radius. We show that the dichotomy regarding the square-integrable solutions known in the continuous time and discrete theory works in the same way for general time scales.
ER -
ŠIMON HILSCHER, Roman and Petr ZEMÁNEK. Overview of Weyl-Titchmarsh theory for second order Sturm-Liouville equations on time scales. \textit{Int. J. Difference Equ.}. Delhi: Research India Publications, 2011, vol.~6, No~1, p.~39-51. ISSN~0973-6069.
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